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Three blocks P, Q and R, each of mass 3 kg, are arranged so that wire A supports the combined weight of blocks Q and R hanging below it, while wire B supports only block R. Each wire has cross-sectional area 0.005 cm² and Young's modulus 2 x 10¹¹ N/m². Friction is negligible and g = 10 m/s². What are the longitudinal strains developed in wires A and B respectively?
- Strain in A = 4 x 10⁻⁴, strain in B = 2 x 10⁻⁴
- Strain in A = 2 x 10⁻⁴, strain in B = 4 x 10⁻⁴
- Strain in A = 6 x 10⁻⁴, strain in B = 3 x 10⁻⁴
- Strain in A = 3 x 10⁻⁴, strain in B = 3 x 10⁻⁴
Correct answer: Strain in A = 6 x 10⁻⁴, strain in B = 3 x 10⁻⁴
Solution
Convert the area: 0.005 cm² = 0.005 x 10⁻⁴ m² = 5 x 10⁻⁷ m², so A * Y = (5 x 10⁻⁷)(2 x 10¹¹) = 1 x 10⁵ N. Wire B carries only block R, tension T_B = m*g = 30 N, giving strain_B = 30 / (1 x 10⁵) = 3 x 10⁻⁴. Wire A carries blocks Q and R, tension T_A = 2*m*g = 60 N, giving strain_A = 60 / (1 x 10⁵) = 6 x 10⁻⁴.
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